Find a Cubic Function $f ( x ) = a x ^ { 3 } - b x ^ { 2 } + c x - d$

question 28

Short Answer

Find a cubic function $f ( x ) = a x ^ { 3 } - b x ^ { 2 } + c x - d$ that has a local maximum value of 112 at 1 and a local minimum value of $- 1,184$ at 7 .

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Definitions:

Standard Normal Distribution

A normal distribution with a mean of zero and a standard deviation of one, used as a basis for comparison in statistical analysis.

Greater Than

A mathematical term used to compare two values where one is larger than the other, often denoted by the symbol '>'.

Z-scores

Standardized scores that measure the distance of a data point from the mean, expressed in units of standard deviation.

Standard Normal Distribution

A normal distribution with a mean of zero and a standard deviation of one.